Film festivals are a key component in the global film industry in terms of trendsetting, publicity, trade, and collaboration. We present an unprecedented analysis of the international film festival circuit, which has so far remained relatively understudied quantitatively, partly due to the limited availability of suitable data sets. We use large-scale data from the Cinando platform of the Cannes Film Market, widely used by industry professionals. We explicitly model festival events as a global network connected by shared films and quantify festivals as aggregates of the metadata of their showcased films. Importantly, we argue against using simple count distributions for discrete labels such as language or production country, as such categories are typically not equidistant. Rather, we propose embedding them in continuous latent vector spaces. We demonstrate how these "festival embeddings" provide insight into changes in programmed content over time, predict festival connections, and can be used to measure diversity in film festival programming across various cultural, social, and geographical variables-which all constitute an aspect of public value creation by film festivals. Our results provide a novel mapping of the film festival circuit between 2009-2021 (616 festivals, 31,989 unique films), highlighting festival types that occupy specific niches, diverse series, and those that evolve over time. We also discuss how these quantitative findings fit into media studies and research on public value creation by cultural industries. With festivals occupying a central position in the film industry, investigations into the data they generate hold opportunities for researchers to better understand industry dynamics and cultural impact, and for organizers, policymakers, and industry actors to make more informed, data-driven decisions. We hope our proposed methodological approach to festival data paves way for more comprehensive film festival studies and large-scale quantitative cultural event analytics in general.